IMO Shortlist 1961 problem 5


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2. travnja 2012.
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Construct a triangle ABC if AC=b, AB=c and \angle AMB=w, where M is the midpoint of the segment BC and w<90. Prove that a solution exists if and only if b \tan{\dfrac{w}{2}} \leq c <b In what case does the equality hold?
Izvor: Međunarodna matematička olimpijada, shortlist 1961